Observer based control for time varying delay systems with unknown inputs

This paper deals with the design of observer based controller for a class of linear time varying delay systems with unknown inputs. We propose to use a completely state observer to reconstruct the state vector for the feedback control purpose. Sufficient and necessary conditions for the existence of such observers based controllers are treated. By using information on asymptotic stability and delay derivative, we develop a method for designing a linear observer based controller ensuring the global uniform asymptotic stabilization for any time delay systems with unknown inputs. Based on Lyapunov stability theory, the design of observer based controller is formulated in terms of linear matrix inequalities (LMIs), it turned into stabilization problem in linear systems. Two design algorithms of observer based controller with unknown inputs for time delay systems are proposed. Numerical examples are given to illustrate the effectiveness of obtained stability conditions.